Evaluation device for providing a transceiver system with performance information thereof

ABSTRACT

An evaluation device is adapted for providing a transceiver system with performance information thereof. The transceiver system includes a transmitter and at least one receiver, and models a channel between the transmitter and the receiver using Nakagami distribution with a fading parameter. The evaluation device includes a signal-to-noise ratio (SNR) setting module, an error rate computing module, and an output module. The SNR setting module is operable to set an average SNR for the channel between the transmitter and the receiver of the transceiver system. The error rate computing module is operable, based upon the fading parameter, the average SNR and a number of the receiver, to compute a bit error rate over the channel between the transmitter and the receiver. The output module is operable to provide the transceiver system with the average SNR and the bit error rate as the performance information of the transceiver system.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to an evaluation device for providing atransceiver system with performance information thereof, moreparticularly to an evaluation device for providing a transceiver system,which models a channel thereof using Nakagami distribution, withperformance information thereof.

2. Description of the Related Art

Referring to FIG. 1, a transceiver system 900 under a multiuserdiversity scheme includes a transmitter 91 and a plurality of receivers92. The transmitter 91 includes a plurality of transmit antennas 93, andthe receiver 92 includes a plurality of receive antennas 94. Under themultiuser diversity scheme, the transmitter 91, such as a base station,is capable of communication with the receivers 92, such as cell phonesof users.

Further, when the transceiver system 900 utilizes a transmit selectivecombining/receive maximum ratio combining (SC/MRC) scheme as an antennascheme thereof, each of the receivers 92 is operable, in advance, toestimate the channels between the transmitter 91 and itself so as todetermine which one of the transmit antennas 93 results in a channelthat has relatively better performance. According to the evaluationresults from the receivers 92, the transmitter 91 is operable tocommunicate with a selected one of the receivers 92, and to transmitsignals to the selected one of the receivers 92 using one of thetransmit antennas 93 corresponding to one of the channels that hasrelatively better performance. Then, the selected one of the receivers92 is operable to weight the signals received by the receive antennas 94thereof so as to optimize the performance of the transceiver system 900.

In “Outage probability of transmitter antenna selection/receiver-MRCover spatially correlated Nakagami-fading channels,” IEEE ICCT'06,November 2006, pages 1-4, Wang B. Y. et al. proposed a method forevaluating performance of a transceiver system under the multiuserdiversity scheme by using Nakagami channels associated with integerfading parameters to simulate an outage probability. However, whenevaluations are conducted in a metropolis, the channels of thetransceiver system usually fade in various levels. Therefore, theNakagami channels only associated with integer fading parameters areinappropriate for simulation of masking, fading, or other interferencesin a metropolis.

SUMMARY OF THE INVENTION

Therefore, an object of the present invention is to provide anevaluation device and method adapted for appropriately evaluatingperformance of a transceiver system by using Nakagami channelsassociated with fading parameters not limited to integers to compute anoutage probability of the transceiver system.

Accordingly, an evaluation device of the present invention is adaptedfor providing a transceiver system with performance information thereof.The transceiver system includes a transmitter and at least one receiver,and models a channel between the transmitter and the receiver usingNakagami distribution with a fading parameter. The evaluation deviceincludes a signal-to-noise ratio (SNR) setting module, an error ratecomputing module, and an output module.

The SNR setting module is operable to set an average SNR for the channelbetween the transmitter and the receiver of the transceiver system. Theerror rate computing module is operable, based upon the fadingparameter, the average SNR and a number of the receiver, to compute abit error rate over the channel between the transmitter and thereceiver. The output module is operable to provide the transceiversystem with the average SNR and the bit error rate as the performanceinformation of the transceiver system.

BRIEF DESCRIPTION OF THE DRAWINGS

Other features and advantages of the present invention will becomeapparent in the following detailed description of the preferredembodiments with reference to the accompanying drawings, of which:

FIG. 1 is a block diagram illustrating a conventional transceiversystem;

FIG. 2 is a block diagram illustrating a single-input single-outputtransceiver system under a multiuser diversity scheme;

FIG. 3 is a block diagram of a first preferred embodiment of anevaluation device of the present invention;

FIG. 4 is a flow chart illustrating an evaluation method implementedusing the evaluation device of the first preferred embodiment;

FIG. 5 is a simulation plot for illustrating a relationship between anaverage signal-to-noise ratio and a bit error rate; and

FIG. 6 is a block diagram illustrating a multiple-input multiple-outputtransceiver system under the multiuser diversity scheme.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Before the present invention is described in greater detail, it shouldbe noted that like elements are denoted by the same reference numeralsthroughout the disclosure.

Referring to FIG. 2, a first preferred embodiment of an evaluationdevice 100 of this invention is adapted for providing a transceiversystem 901 with performance information thereof. In this embodiment, thetransceiver system 901 is a single-input single-output transceiversystem under a multiuser diversity scheme, and includes a transmitter(Tx) and a number K (K>1) of receivers (Rx). The transceiver system 901utilizes a modulation scheme, such as a binary phase-shift keying (BPSK)scheme, for conveying data. In practice, the transmitter (Tx) is a basestation, and each of the receivers (Rx) is a cell phone of a user. Forillustrative purpose, the transceiver system 901 includes three (K=3) ofthe receivers (Rx) in FIG. 2.

The transmitter (Tx) includes a transmit antenna (T1). Each of thereceivers (Rx) includes a receive antenna (R1) and a channel estimator(R2). In this embodiment, the evaluation device 100 is operable to modela channel between the transmit antenna (T1) and the receive antenna (R1)of each of the receivers (Rx) using Nakagami distribution with anarbitrary positive fading parameter m.

The channel estimator (R2) of each of the receivers (Rx) is operable toprovide the transmitter (Tx) with a transmission quality of the channelcorresponding to each of the receivers (Rx). Then, according to thetransmission quality, the transmitter (Tx) is operable to determinewhich one of the receivers (Rx) will be selected as a communicationtarget, and to transmit a signal through the transmit antenna (T1) fortransmission of the signal to the communication target. Then, thecommunication target is operable to receive the signal as a receivedsignal through the receive antenna (R1) thereof. It should be noted thatthe communication target is one of the receivers (Rx) that demonstratesthe greatest transmission quality with the transmitter (Tx).

When the fading parameter m of Nakagami distribution is greater than orequal to ½, a bit error rate of BPSK in the received signal may becalculated based upon Equation (1).

$\begin{matrix}{P_{BER} = {\frac{1}{2\sqrt{\pi}}{\sum\limits_{n = 0}^{\infty}\frac{{\alpha_{n} \cdot \left( {m/\overset{\_}{Q}} \right)^{{mK} + n}}{\Gamma\left( {{mK} + n + 0.5} \right)}}{\left( {1 + {{mK}/\overset{\_}{Q}}} \right)^{{mK} + n + 0.5}}}}} & (1)\end{matrix}$

In Equation (1), Q is an average signal-to-noise ration (SNR) of thechannel, Γ(z) is a Gamma function

(Γ(z) = ∫₀^(∞)t^(z − 1)𝕖^(−t) 𝕕t)for an arbitrary positive number z,

${\alpha_{0} = \left\lbrack \frac{1}{\Gamma\left( {m + 1} \right)} \right\rbrack^{K}},{\alpha_{n} = {\frac{1}{n}{\sum\limits_{j = 1}^{n}\left\lbrack {\frac{{j\left( {K + 1} \right)} - n}{\left( {m + 1} \right)_{j}} \cdot \alpha_{n - j}} \right\rbrack}}}$for a positive integer n, and (m+1)_(j)=Γ(m+1+j)/Γ(m+1). For details ofthe Gamma function Γ(z), one may refer to Equation (8.310.1) in “Tableof Integrals, Series, and Products” (Academic Press, New York, 1994,5^(th) edition).

It could be appreciated from the foregoing that α_(n) are a sequence ofrapidly decreasing convergent numbers, that is to say, α_(n-1) is muchgreater than α_(n). Therefore, when the average SNR Q is much greaterthan 1, i.e., greater than a predetermined value, Equation (1) can besimplified as Equation (2). For the procedure of this simplification,one may refer to “A simple and general parameterization quantifyingperformance in fading channels,” Wang Z. et al., IEEE Trans. Commun.,August 2003, 51(8), pages 1389-1398.

$\begin{matrix}{P_{BER} \approx \frac{{\Gamma\left( {{mK} + 0.5} \right)} \cdot \left( {m/\overset{\_}{Q}} \right)^{mK}}{2{\sqrt{\pi}\left\lbrack {\Gamma\left( {m + 1} \right)} \right\rbrack}^{K}}} & (2)\end{matrix}$

When the fading parameter m of Nakagami distribution is a positiveinteger, the bit error rate of BPSK in the received signal may becalculated based upon Equation (3).

$\begin{matrix}{P_{BER} = {\frac{1}{2\sqrt{\pi}}{\sum\limits_{i = 0}^{K}{\begin{pmatrix}K \\i\end{pmatrix}\left( {- 1} \right)^{i}{\sum\limits_{n = 0}^{i{({m - 1})}}\frac{{\beta_{n} \cdot \left( {m/\overset{\_}{Q}} \right)^{n}}{\Gamma\left( {n + 0.5} \right)}}{\left( {1 + {m\;{i/\overset{\_}{Q}}}} \right)^{n + 0.5}}}}}}} & (3)\end{matrix}$

In Equation (3), β₀=1,

$\beta_{n} = {\frac{1}{n}{\sum\limits_{j = 1}^{\min{({n,{m - 1}})}}\left\lbrack {\frac{{j\left( {i + 1} \right)} - n}{j!} \cdot \beta_{n - j}} \right\rbrack}}$for a positive integer n, and

$\begin{pmatrix}K \\i\end{pmatrix} = {\frac{K!}{{i!}{\left( {K - i} \right)!}}.}$

As shown in FIG. 2, in this embodiment, the evaluation device 100 isadapted for analyzing the received signal in the transceiver system 901modeling the channels using the Nakagami distribution, and each of thechannels has the same average SNR Q.

Referring to FIG. 3, the evaluation device 100 includes an SNR settingmodule 1, an error rate computing module 2 coupled to the SNR settingmodule 1, a threshold value computing module 4, an outage probabilitycomputing module 5 coupled to the SNR setting module 1 and the thresholdvalue computing module 4, and an output module 3 coupled to the errorrate computing module 2 and the outage probability computing module 5.

The SNR setting module 1 is operable to set the average SNR Q for eachof the channels between the transmitter (Tx) and the receivers (Rx) ofthe transceiver system 901. The threshold value computing module 4 isoperable to compute a threshold value λ based upon a given capacity R.The error rate computing module 2 is operable to compute the bit errorrate P_(BER) of the received signal based upon the fading parameter m,the average SNR Q and the number K of the receivers (Rx). The outageprobability computing module 5 is operable, based upon the fadingparameter m, the number K of the receivers (Rx), the average SNR Q andthe threshold value λ, to compute an outage probability of thetransceiver system 901 corresponding to the given capacity R. Then, theoutput module 3 is operable to provide the transceiver system 901 withthe average SNR Q, the bit error rate P_(BER) and the outage probabilityas the performance information of the transceiver system 901.

FIG. 4 shows a flow chart of an evaluation method implemented by theevaluation device 100. The evaluation method includes the followingsteps.

In step 71, the threshold value computing module 4 is operable tocompute the threshold value λ based upon the given capacity R(λ=2^(R)−1).

In step 72, the SNR setting module 1 is operable to set each of thechannels with the same average SNR Q.

In step 73, the error rate computing module 2 is operable to compute thebit error rate P_(BER) based upon the fading parameter m, the averageSNR Q and the number K of the receivers (Rx).

In practice, the error rate computing module 2 is operable in advance todetermine whether the fading parameter m is a positive integer. Theerror rate computing module 2 is operable to compute the bit error rateP_(BER) based upon Equation (3) when the determination is affirmative,and to compute the bit error rate P_(BER) based upon Equation (1) or (2)when otherwise. In particular, when the fading parameter m is not apositive integer, the error rate computing module 2 is operable tocompute the bit error rate P_(BER) based upon Equation (2) if theaverage SNR Q is greater than a predetermined value, and to compute thebit error rate P_(BER) based upon Equation (1) if the average SNR Q isnot greater than the predetermined value. Further, in practice, it isimpractical to calculate the summation of the infinite series

$\left( \sum\limits_{n = 0}^{\infty} \right)$in Equation (1). Therefore, the error rate computing module 2 isoperable to compute a limited number of the series. In this embodiment,the error rate computing module 2 is operable to compute the series forn=0˜50 when computing the summation.

From Equations (1) to (3), it can be appreciated that the error ratecomputing module 2 computes the bit error rate P_(BER) based upon theaverage SNR Q, the fading parameter m, and the number K of the receivers(Rx). Certainly, in other embodiments, the error rate computing module 2may be operable in advance to determine whether the fading parameter mis greater than or equal to ½, and to compute the bit error rate P_(BER)based upon Equation (1) or (2) when affirmative.

In step 74, the outage probability computing module 5 is operable, basedupon the fading parameter m, the number K of the receivers (Rx), theaverage SNR Q and the threshold value λ, to compute the outageprobability of the transceiver system 901 corresponding to the givencapacity R.

For the procedure of the computation of the outage probability, one mayrefer to “Outage analysis of MIMO systems with multiuser diversity overNakagami-m fading channels,” 2009 Fundamental Academic Conference ofR.O.C. Military Academy, pages EE.115-EE.124. Therefore, details of thiscomputation will be omitted herein for the sake of brevity.

It should be noted that step 74 could be implemented before orsimultaneously with step 73 in other embodiments.

In step 75, the output module 3 is operable to determine whether thereis an instruction of setting another average SNR. The flow goes backstep 72 when the determination is affirmative, and goes to step 75 whenotherwise.

In step 76, the output module 3 is operable to provide the transceiversystem 901 with the bit error rate P_(BER) and the outage probabilitycorresponding to each of the average SNRs Q set in step 72 as theperformance information of the transceiver system 901.

Taking FIG. 5 as an example, it is assumed that K=2 and m=0.7, and thebit error rates P_(BER) corresponding to the respective average SNRs Qare computed based upon Equation (1). The symbols ◯ in FIG. 5 representthe bit error rates P_(BER) computed using the evaluation device 100 ofthis embodiment. It can be appreciated that the bit error rates P_(BER)increase with the average SNRs Q, that is to say, transmission error ofthe transceiver system 901 decreases and the performance thereof isrelatively better.

Referring to FIG. 6, a second preferred embodiment of an evaluationdevice 200 of this invention is adapted for providing a transceiversystem 902 with performance information thereof. The transceiver system902 is a multiple-input multiple-output (MIMO) transceiver system undera multiuser diversity scheme, and includes a transmitter (Tx) and anumber K (K>1) of receivers (Rx). The transceiver system 902 utilizes amodulation scheme similar to that of the first preferred embodiment(e.g., the BPSK scheme) for conveying data. In this embodiment, thetransceiver system 902 utilizes a transmit selective combining/receiveselective combining (SC/SC) scheme as an antenna scheme thereof. Inpractice, the transmitter (Tx) is a base station, and each of thereceivers (Rx) is a cell phone of a user. For illustrative purpose, thetransceiver system 902 includes three (K=3) of the receivers (Rx) inFIG. 6.

The transmitter (Tx) includes a number L_(T) (L_(T)>1) of transmitantennas (T1), and a diversity unit (T2). Each of the receivers (Rx)includes a number L_(R) (L_(R)>1) of receive antennas (R1), a synthesisunit (R3), and a channel estimator (R2). In this embodiment, theevaluation device 200 is operable to model channels between the transmitantennas (T1) and the receive antennas (R1) using Nakagami distributionwith an arbitrary positive fading parameter m.

In such a SC/SC scheme, there are a number L_(T)×L_(R) of possiblechannels for each of the receivers (Rx), and each of the channels isdefined by one of the transmit antennas (T1) and one of the receiveantennas (R1). The channel estimator (R2) of each of the receivers (Rx)is operable to provide the transmitter (Tx) with transmission qualitiesof the possible channels corresponding to each of the receivers (Rx).Then, according to the transmission qualities, the diversity unit (T2)of the transmitter (Tx) is operable to determine which one of thereceivers (Rx) will be selected as a communication target, and todetermine which one of the transmit antennas (T1) will be used totransmit signals. The diversity unit (T2) is further operable totransmit the signals to a selected one of the transmit antennas (T1) fortransmission of the signals to the communication target. It should benoted that the communication target is one of the receivers (Rx) thatdemonstrates the greatest transmission quality with the transmitter(Tx), and the selected one of the transmit antennas (T1) is capable ofreaching such transmission quality.

After the selected one of the receivers (Rx), which is selected as thecommunication target, receives the signals from the transmitter (Tx)through the receive antennas (R1) thereof, the signals are transmittedto the synthesis unit (R3) of the selected one of the receivers (Rx).The synthesis unit (R3) is operable to select one of the signalsreceived by the receive antennas (R1) for analysis.

When the fading parameter m of Nakagami distribution is greater than orequal to ½, the bit error rate of BPSK in the selected one of thesignals received by the receive antennas (R1) may be calculated basedupon Equation (4).

$\begin{matrix}{P_{BER} = {\frac{1}{2\sqrt{\pi}}{\sum\limits_{n = 0}^{\infty}\frac{{\alpha_{n} \cdot \left( {m/\overset{\_}{Q}} \right)^{{{mKL}_{T}L_{R}} + n}}{\Gamma\left( {{{mKL}_{T}L_{R}} + n + 0.5} \right)}}{\left( {1 + {{mKL}_{T}{L_{R}/\overset{\_}{Q}}}} \right)^{{{mKL}_{T}L_{R}} + n + 0.5}}}}} & (4)\end{matrix}$

In Equation (4),

${\alpha_{0} = \left\lbrack \frac{1}{\Gamma\left( {m + 1} \right)} \right\rbrack^{{KL}_{T}L_{R}}},{\alpha_{n} = {\frac{1}{n}{\sum\limits_{j = 1}^{n}\left\lbrack {\frac{{j\left( {{{KL}_{T}L_{R}} + 1} \right)} - n}{\left( {m + 1} \right)_{j}} \cdot \alpha_{n - j}} \right\rbrack}}}$for a positive integer n, and (m+1)_(j)=Γ(m+1+j)/Γ(m+1).

It could be appreciated from the foregoing that α_(n) are a sequence ofrapidly decreasing convergent numbers, that is to say, α_(n-1) is muchgreater than α_(n). Therefore, when the average SNR Q is much greaterthan 1, i.e., greater than a predetermined value, Equation (4) can besimplified as Equation (5). For the procedure of this simplification,one may refer to “A simple and general parameterization quantifyingperformance in fading channels,” Wang Z. et al., IEEE Trans. Commun.,August 2003, 51(8), pages 1389-1398.

$\begin{matrix}{P_{BER} \approx \frac{{\Gamma\left( {{{mKL}_{T}L_{R}} + 0.5} \right)} \cdot \left( {m/\overset{\_}{Q}} \right)^{{mKL}_{T}L_{R}}}{2{\sqrt{\pi}\left\lbrack {\Gamma\left( {m + 1} \right)} \right\rbrack}^{{KL}_{T}L_{R}}}} & (5)\end{matrix}$

When the fading parameter m of Nakagami distribution is a positiveinteger, the bit error rate of BPSK in the selected one of the signalsreceived by the receive antennas (R1) may be calculated based uponEquation (6).

$\begin{matrix}{P_{BER} = {\frac{1}{2\sqrt{\pi}}{\sum\limits_{i = 0}^{{KL}_{T}L_{R}}{\begin{pmatrix}{{KL}_{T}L_{R}} \\i\end{pmatrix}\left( {- 1} \right)^{i}{\sum\limits_{n = 0}^{i{({m - 1})}}\frac{{\beta_{n} \cdot \left( {m/\overset{\_}{Q}} \right)^{n}}{\Gamma\left( {n + 0.5} \right)}}{\left( {1 + {m\;{i/\overset{\_}{Q}}}} \right)^{n + 0.5}}}}}}} & (6)\end{matrix}$

In Equation (6), β₀=1,

$\beta_{n} = {\frac{1}{n}{\sum\limits_{j = 1}^{\min{({n,{m - 1}})}}\left\lbrack {\frac{{j\left( {i + 1} \right)} - n}{j!} \cdot \beta_{n - j}} \right\rbrack}}$for a positive integer n, and

$\begin{pmatrix}{{KL}_{T}L_{R}} \\i\end{pmatrix} = {\frac{\left( {{KL}_{T}L_{R}} \right)!}{{i!}{\left( {{{KL}_{T}L_{R}} - i} \right)!}}.}$

The second preferred embodiment of the evaluation device 200 of thisinvention has a configuration similar to that of the first preferredembodiment, and also includes the SNR setting module 1, the error ratecomputing module 2, the output module 3, the threshold value computingmodule 4 and the outage probability computing module 5 shown in FIG. 3.Operations of the modules of the evaluation device 200 in thisembodiment are also similar to those of the first preferred embodiment.

In this embodiment, the error rate computing module 2 is operable, instep 73 of the flow chart shown in FIG. 4, to compute the bit error rateP_(BER) based upon the fading parameter m, the average SNR Q, the numberL_(T) of the transmit antennas (T1), the number L_(R) of the receiveantennas (R1), and the number K of the receivers (Rx).

In practice, the error rate computing module 2 is operable in advance todetermine whether the fading parameter m is a positive integer. Theerror rate computing module 2 is operable to compute the bit error rateP_(BER) based upon Equation (6) when the determination is affirmative,and to compute the bit error rate P_(BER) based upon Equation (4) or (5)when otherwise.

Certainly, in other embodiments, the error rate computing module 2 maybe operable in advance to determine whether the fading parameter m isgreater than or equal to ½, and to compute the bit error rate P_(BER)based upon Equation (4) or (5) when affirmative.

In particular, when the fading parameter m is not a positive integer,the error rate computing module 2 is operable to compute the bit errorrate P_(BER) based upon Equation (5) if the average SNR Q is greaterthan a predetermined value, and to compute the bit error rate P_(BER)based upon Equation (4) if the average SNR Q is not greater than thepredetermined value. Further, in practice, it is impractical tocalculate the summation of the infinite series

$\left( \sum\limits_{n = 0}^{\infty} \right)$in Equation (4). Therefore, the error rate computing module 2 isoperable to compute a limited number of the series. In this embodiment,the error rate computing module 2 is operable to compute the series forn=0˜50 when computing the summation.

As an example, when it is assumed that L_(T)=1, L_(R)=4, K=2 and m=0.7,the bit error rates P_(BER) corresponding to the respective average SNRsQ may be computed based upon Equation (4) represented by the symbols □in FIG. 5. The information of the symbols □ could serve as theperformance information of the transceiver system 902 in step 76 of theflow chart shown in FIG. 4.

Referring once again to FIG. 6, a third preferred embodiment of anevaluation device 300 of this invention has a configuration similar tothat of the second preferred embodiment, and is adapted for providingthe MIMO transceiver system 902 with the performance informationthereof. In this embodiment, the transceiver system 902 utilizes atransmit selective combining/receive maximum ratio combining (SC/MRC)scheme as an antenna scheme thereof.

In such a SC/MRC scheme, the channel estimator (R2) of each of thereceivers (Rx) is operable to provide the transmitter (Tx) withtransmission qualities of the possible channels corresponding to each ofthe receivers (Rx). Then, according to the transmission qualities, thediversity unit (T2) of the transmitter (Tx) is operable to determinewhich one of the receivers (Rx) will be selected as the communicationtarget, and to determine which one of the transmit antennas (T1) will beused to transmit signals. The diversity unit (T2) is further operable totransmit the signals to a selected one of the transmit antennas (T1) fortransmission of the signals to the communication target.

After the selected one of the receivers (Rx), which is selected as thecommunication target, receives the signals from the transmitter (Tx)through the receive antennas (R1) thereof, the signals are transmittedto the synthesis unit (R3) of the selected one of the receivers (Rx).According to the transmission qualities of the channels between theselected one of the transmit antennas (T1) and the receive antennas(R1), the synthesis unit (R3) is operable to weight the signals receivedby the receive antennas (R1) so as to obtain a synthesized signal.

When the fading parameter m of Nakagami distribution is greater than orequal to ½, the bit error rate of BPSK in the synthesized signal may becalculated based upon Equation (7).

$\begin{matrix}{P_{BER} = {\frac{1}{2\sqrt{\pi}}{\sum\limits_{n = 0}^{\infty}\frac{{\alpha_{n} \cdot \left( {m/\overset{\_}{Q}} \right)^{{{mKL}_{T}L_{R}} + n}}{\Gamma\left( {{{mKL}_{T}L_{R}} + n + 0.5} \right)}}{\left( {1 + {{mKL}_{T}/\overset{\_}{Q}}} \right)^{{{mKL}_{T}L_{R}} + n + 0.5}}}}} & (7)\end{matrix}$

In Equation (7),

${\alpha_{0} = \left\lbrack \frac{1}{\Gamma\left( {m + 1} \right)} \right\rbrack^{{KL}_{T}}},{\alpha_{n} = {\frac{1}{n}{\sum\limits_{j = 1}^{n}\left\lbrack {\frac{{j\left( {{KL}_{T} + 1} \right)} - n}{\left( {{m\; L_{R}} + 1} \right)_{j}} \cdot \alpha_{n - j}} \right\rbrack}}}$for a positive integer n, and (mL_(R)+1)_(j)=Γ(mL_(R)+1+j)/Γ(mL_(R)+1).

Similar to the foregoing description in connection with the secondpreferred embodiment, Equation (7) can be simplified as Equation (8)when the average SNR Q is much greater than 1, i.e., greater than apredetermined value.

$\begin{matrix}{P_{BER} = \frac{{\Gamma\left( {{{mKL}_{T}/\overset{\_}{Q}} + 0.5} \right)} \cdot \left( {m\; L_{R}} \right)^{{mKL}_{T}/\overset{\_}{Q}}}{2{\sqrt{\pi}\left\lbrack {\Gamma\left( {{m/\overset{\_}{Q}} + 1} \right)} \right\rbrack}^{{KL}_{T}}}} & (8)\end{matrix}$

When the fading parameter m of Nakagami distribution is a positiveinteger, the bit error rate of BPSK in the synthesized signal may becalculated based upon Equation (9).

$\begin{matrix}{P_{BER} = {\frac{1}{2\sqrt{\pi}}{\sum\limits_{i = 0}^{{KL}_{T}}{\begin{pmatrix}{KL}_{T} \\i\end{pmatrix}\left( {- 1} \right)^{i}{\sum\limits_{n = 0}^{i{({{m\; L_{R}} - 1})}}\frac{{\beta_{n} \cdot \left( {m/\overset{\_}{Q}} \right)^{n}}{\Gamma\left( {n + 0.5} \right)}}{\left( {1 + {m\;{i/\overset{\_}{Q}}}} \right)^{n + 0.5}}}}}}} & (9)\end{matrix}$

In Equation (9), β₀=1,

$\beta_{n} = {\frac{1}{n}{\sum\limits_{j = 1}^{\min{({n,{{m\; L_{R}} - 1}})}}\left\lbrack {\frac{{j\left( {i + 1} \right)} - n}{j!} \cdot \beta_{n - j}} \right\rbrack}}$for a positive integer n, and

$\begin{pmatrix}{KL}_{T} \\i\end{pmatrix} = {\frac{\left( {KL}_{T} \right)!}{{i!}{\left( {{KL}_{T} - i} \right)!}}.}$

The third preferred embodiment of the evaluation device 300 of thisinvention has a configuration similar to that of the first preferredembodiment, and also includes the SNR setting module 1, the error ratecomputing module 2, the output module 3, the threshold value computingmodule 4 and the outage probability computing module 5 shown in FIG. 3.Operations of the modules of the evaluation device 300 in thisembodiment are also similar to those the first preferred embodiment.

In this embodiment, the error rate computing module 2 is operable, instep 73 of the flow chart shown in FIG. 4, to compute the bit error rateP_(BER) based upon the fading parameter m, the average SNR Q, the numberL_(T) of the transmit antennas (T1), the number L_(R) of the receiveantennas (R1), and the number K of the receivers (Rx).

In practice, the error rate computing module 2 is operable in advance todetermine whether the fading parameter m is a positive integer. Theerror rate computing module 2 is operable to compute the bit error rateP_(BER) based upon Equation (9) when the determination is affirmative,and to compute the bit error rate P_(BER) based upon Equation (7) or (8)when otherwise.

Certainly, in other embodiments, the error rate computing module 2 maybe operable in advance to determine whether the fading parameter m isgreater than or equal to ½, and to compute the bit error rate P_(BER)based upon Equation (7) or (8) when affirmative.

In particular, when the fading parameter m is not a positive integer,the error rate computing module 2 is operable to compute the bit errorrate P_(BER) based upon Equation (8) if the average SNR Q is greaterthan a predetermined value, and to compute the bit error rate P_(BER)based upon Equation (7) if the average SNR Q is not greater than thepredetermined value. Further, in practice, it is impractical tocalculate the summation of the infinite series

$\left( \sum\limits_{n = 0}^{\infty} \right)$in Equation (7). Therefore, the error rate computing module 2 isoperable to compute a limited number of the series. In this embodiment,the error rate computing module 2 is operable to compute the series forn=0˜50 when computing the summation.

As an example, when it is assumed that L_(T)=1, L_(R)=4, K=2 and m=0.7,the bit error rates P_(BER) corresponding to the respective average SNRsQ may be computed based upon Equation (7) represented by the symbols ∇in FIG. 5. The information of the symbols ∇ could serve as theperformance information of the transceiver system 902 in step 76 of theflow chart shown in FIG. 4.

Referring again to FIG. 6, a fourth preferred embodiment of anevaluation device 400 of this invention has a configuration similar tothat of the second preferred embodiment, and is adapted for providingthe MIMO transceiver system 902 with the performance informationthereof. In this embodiment, the transceiver system 902 utilizes aspace-time block codes (STBC) scheme as an antenna scheme thereof.

In such a STBC scheme, the channel estimator (R2) of each of thereceivers (Rx) is operable to provide the transmitter (Tx) withtransmission qualities of the possible channels corresponding to each ofthe receivers (Rx). Then, according to the transmission qualities, thediversity unit (T2) of the transmitter (Tx) is operable to determinewhich one of the receivers (Rx) will be selected as the communicationtarget. The diversity unit (T2) is further operable to encode ato-be-transmitted signal using space-time block coding, and to transmitthe coded signal to the communication target through each of thetransmit antennas (T1).

After the selected one of the receivers (Rx), which is selected as thecommunication target, receives the coded signals from the transmitter(Tx) through the receive antennas (R1) thereof, the coded signals aretransmitted to the synthesis unit (R3) of the selected one of thereceivers (Rx). Then, the synthesis unit (R3) is operable to decode thecoded signals received by the receive antennas (R1) so as to obtain adecoded signal. Since the space-time block coding/decoding is well knownto those skilled in the art, details thereof will be omitted herein forthe sake of brevity.

When the fading parameter m of Nakagami distribution is greater than orequal to ½, the bit error rate of BPSK in the decoded signal may becalculated based upon Equation (10).

$\begin{matrix}{P_{BER} = {\frac{1}{2\sqrt{\pi}}{\sum\limits_{n = 0}^{\infty}\frac{{\alpha_{n} \cdot \left( {{mL}_{T}/\overset{\_}{Q}} \right)^{{{mKL}_{T}L_{R}} + n}}{\Gamma\left( {{{mKL}_{T}L_{R}} + n + 0.5} \right)}}{\left( {1 + {{mKL}_{T}/\overset{\_}{Q}}} \right)^{{{mKL}_{T}L_{R}} + n + 0.5}}}}} & (10)\end{matrix}$

In Equation (10),

${\alpha_{0} = \left\lbrack \frac{1}{\Gamma\left( {{m\; L_{T}L_{R}} + 1} \right)} \right\rbrack^{K}},{\alpha_{n} = {\frac{1}{n}{\sum\limits_{j = 1}^{n}\left\lbrack {\frac{{j\left( {K + 1} \right)} - n}{\left( {{m\; L_{T}L_{R}} + 1} \right)_{j}} \cdot \alpha_{n - j}} \right\rbrack}}}$for a positive integer n, and(mL_(T)L_(R)+1)_(j)=Γ(mL_(T)L_(R)+1+j)/Γ(mL_(T)L_(R)+1).

Similar to the foregoing description in connection with the secondpreferred embodiment, Equation (10) can be simplified as Equation (11)when the average SNR Q is much greater than 1, i.e., greater than apredetermined value.

$\begin{matrix}{P_{BER} \approx \frac{{\Gamma\left( {{{mKL}_{T}L_{R}} + 0.5} \right)} \cdot \left( {{mL}_{T}/\overset{\_}{Q}} \right)^{{mKL}_{T}L_{R}}}{2{\sqrt{\pi}\left\lbrack {\Gamma\left( {{{mL}_{T}L_{R}} + 1} \right)} \right\rbrack}^{K}}} & (11)\end{matrix}$

When the fading parameter m of Nakagami distribution is a positiveinteger, the bit error rate of BPSK in the decoded signal may becalculated based upon Equation (12).

$\begin{matrix}{P_{BER} = {\frac{1}{2\sqrt{\pi}}{\sum\limits_{i = 0}^{K}\;{\begin{pmatrix}K \\i\end{pmatrix}\left( {- 1} \right)^{i}{\sum\limits_{n = 0}^{i{({{{mL}_{T}L_{R}} - 1})}}\;\frac{{\beta_{n} \cdot \left( {{mL}_{T}/\overset{\_}{Q}} \right)^{n}}{\Gamma\left( {n + 0.5} \right)}}{\left( {1 + {{miL}_{T}/\overset{\_}{Q}}} \right)^{n + 0.5}}}}}}} & (12)\end{matrix}$

In Equation (12),

${\begin{pmatrix}K \\i\end{pmatrix} = \frac{(K)!}{{i!}{\left( {K - i} \right)!}}},$β₀=1, and

$\beta_{n} = {\frac{1}{n}{\sum\limits_{j = 1}^{\min{({n,{{{mL}_{T}L_{R}} - 1}})}}\;\left\lbrack {\frac{{j\left( {i + 1} \right)} - n}{j!} \cdot \beta_{n - j}} \right\rbrack}}$for a positive integer n.

The fourth preferred embodiment of the evaluation device 400 of thisinvention has a configuration similar to that of the first preferredembodiment, and also includes the SNR setting module 1, the error ratecomputing module 2, the output module 3, the threshold value computingmodule 4 and the outage probability computing module 5 shown in FIG. 3.Operations of the modules of the evaluation device 400 in thisembodiment are also similar to those of the first preferred embodiment.

In this embodiment, the error rate computing module 2 is operable, instep 73 of the flow chart shown in FIG. 4, to compute the bit error rateP_(BER) based upon the fading parameter m, the average SNR Q, the numberL_(T) of the transmit antennas (T1), the number L_(R) of the receiveantennas (R1), and the number K of the receivers (Rx).

In practice, the error rate computing module 2 is operable in advance todetermine whether the fading parameter m is a positive integer. Theerror rate computing module 2 is operable to compute the bit error rateP_(BER) based upon Equation (12) when the determination is affirmative,and to compute the bit error rate P_(BER) based upon Equation (10) or(11) when otherwise.

Certainly, in other embodiments, the error rate computing module 2 maybe operable in advance to determine whether the fading parameter m isgreater than or equal to ½, and to compute the bit error rate P_(BER)based upon Equation (10) or (11) when affirmative.

In particular, when the fading parameter m is not a positive integer,the error rate computing module 2 is operable to compute the bit errorrate P_(BER) based upon Equation (11) if the average SNR Q is greaterthan a predetermined value, and to compute the bit error rate P_(BER)based upon Equation (10) if the average SNR Q is not greater than thepredetermined value. Further, in practice, it is impractical tocalculate the summation of the infinite series

$\left( \sum\limits_{n = 0}^{\infty}\; \right)$in Equation (10). Therefore, the error rate computing module 2 isoperable to compute a limited number of the series. In this embodiment,the error rate computing module 2 is operable to compute the series forn=0˜50 when computing the summation.

As an example, when it is assumed that L_(T)=1, L_(R)=4, K=2 and m=0.7,the bit error rates P_(BER) corresponding to the respective average SNRsQ may be computed based upon Equation (10) represented by the symbols ⋄in FIG. 5. The information of the symbols ⋄ could serve as theperformance information of the transceiver system 902 in step 76 of theflow chart shown in FIG. 4.

In the disclosed embodiments, the output module 3 is operable to providethe transceiver system 901, 902 with the bit error rate P_(BER) and theoutage probability corresponding to each of the average SNRs Q set instep 72 as the performance information of the transceiver system 901,902. However, in other embodiments, the output module 3 may be operableto provide only the bit error rate P_(BER) corresponding to each of theaverage SNRs Q, or only the outage probability corresponding to each ofthe average SNRs Q as the performance information. Further, Equations(1) to (12) are still practical when the number of the receivers (Rx) isequal to 1 (K=1).

In conclusion, the fading parameter m of Nakagami channels is notlimited to a positive integer in the present invention. The error ratecomputing module 2 is capable of computing the bit error rate P_(BER)with the fading parameter m that is an arbitrary positive integer, orthat is equal to or greater than ½. Therefore, the evaluation deviceaccording to this invention is suitable for simulation of the channelsof the transceiver system with various fading levels in a metropolis.Therefore, the evaluation device according to the present invention issuitable for simulating the performance of the transceiver system in ametropolis.

While the present invention has been described in connection with whatare considered the most practical and preferred embodiments, it isunderstood that this invention is not limited to the disclosedembodiments but is intended to cover various arrangements includedwithin the spirit and scope of the broadest interpretation so as toencompass all such modifications and equivalent arrangements.

1. An evaluation device adapted for providing a transceiver system withperformance information thereof, the transceiver system including atransmitter and a number K of receivers, and modeling a channel betweenthe transmitter and each of the receivers using Nakagami distributionwith a fading parameter, said evaluation device comprising: asignal-to-noise ratio (SNR) setting module operable to set an averageSNR for the channel between the transmitter and each of the receivers ofthe transceiver system; an error rate computing module operable tocompute a bit error rate over the channel between the transmitter andeach of the receivers, when the fading parameter m is greater than orequal to ½, said error rate computing module being operable to computethe bit error rate P_(BER) based upon${P_{BER} = {\frac{1}{2\sqrt{\pi}}{\sum\limits_{n = 0}^{n^{\prime}}\;\frac{{\alpha_{n} \cdot \left( {m/\overset{\_}{Q}} \right)^{{mK} + n}}{\Gamma\left( {{mK} + n + 0.5} \right)}}{\left( {1 + {{mK}/\overset{\_}{Q}}} \right)^{{mK} + n + 0.5}}}}},$where Q is the average SNR,${\alpha_{0} = \left\lbrack \frac{1}{\Gamma\left( {m + 1} \right)} \right\rbrack^{K}},{\alpha_{n} = {\frac{1}{n}{\sum\limits_{j = 1}^{n}\;\left\lbrack {\frac{{j\left( {K + 1} \right)} - n}{\left( {m + 1} \right)_{j}} \cdot \alpha_{n - j}} \right\rbrack}}}$for a positive integer n, (m+1)_(j)=Γ(m+1+j)/Γ(m+1),Γ(z) = ∫₀^(∞)t^(z − 1)𝕖^(−t) 𝕕t for an arbitrary positive number z, andn′ is an arbitrary positive integer; and an output module operable toprovide the transceiver system with the average SNR and the bit errorrate as the performance information of the transceiver system.
 2. Theevaluation device as claimed in claim 1, wherein when the fadingparameter m is greater than or equal to ½, and the average SNR Q isgreater than a predetermined value, said error rate computing module isoperable to compute the bit error rate P_(BER) based upon${P_{BER} = \frac{{\Gamma\left( {{mK} + 0.5} \right)} \cdot \left( {m/\overset{\_}{Q}} \right)^{mK}}{2{\sqrt{\pi}\left\lbrack {\Gamma\left( {m + 1} \right)} \right\rbrack}^{K}}},$Where Γ(z) = ∫₀^(∞)t^(z − 1)𝕖^(−t) 𝕕t for an arbitrary positive numberz.
 3. The evaluation device as claimed in claim 1, wherein when thefading parameter m is a positive integer, said error rate computingmodule is operable to compute the bit error rate P_(BER) based upon${P_{BER} = {\frac{1}{2\sqrt{\pi}}{\sum\limits_{i = 0}^{K}\;{\begin{pmatrix}K \\i\end{pmatrix}\left( {- 1} \right)^{i}{\sum\limits_{n = 0}^{i{({m - 1})}}\;\frac{{\beta_{n} \cdot \left( {m/\overset{\_}{Q}} \right)^{n}}{\Gamma\left( {n + 0.5} \right)}}{\left( {1 + {{mi}/\overset{\_}{Q}}} \right)^{n + 0.5}}}}}}},$where Q is the average SNR, β₀=1,$\beta_{n} = {\frac{1}{n}{\sum\limits_{j = 1}^{\min{({n,{m - 1}})}}\;\left\lbrack {\frac{{j\left( {i + 1} \right)} - n}{j!} \cdot \beta_{n - j}} \right\rbrack}}$for a positive integer n, ${\begin{pmatrix}K \\i\end{pmatrix} = \frac{(K)!}{{i!}{\left( {K - i} \right)!}}},$ andΓ(z) = ∫₀^(∞)t^(z − 1)𝕖^(−t) 𝕕t for an arbitrary positive number z. 4.The evaluation device as claimed in claim 1, each of the receivershaving a number L_(R) of receive antennas under a transmit selectivecombining/receive selective combining (SC/SC) scheme, the transmitterhaving a number L_(T) of transmit antennas, wherein when the fadingparameter m is greater than or equal to ½, said error rate computingmodule is operable to compute the bit error rate P_(BER) based upon${P_{BER} = {\frac{1}{2\sqrt{\pi}}{\sum\limits_{n = 0}^{n^{\prime}}\;\frac{{\alpha_{n} \cdot \left( {m/\overset{\_}{Q}} \right)^{{{mKL}_{T}L_{R}} + n}}{\Gamma\left( {{{mKL}_{T}L_{R}} + n + 0.5} \right)}}{\left( {1 + {{mKL}_{T}{L_{R}/\overset{\_}{Q}}}} \right)^{{{mKL}_{T}L_{R}} + n + 0.5}}}}},$where Q is the average SNR,${\alpha_{0} = \left\lbrack \frac{1}{\Gamma\left( {m + 1} \right)} \right\rbrack^{{KL}_{T}L_{R}}},{\alpha_{n} = {\frac{1}{n}{\sum\limits_{j = 1}^{n}\;\left\lbrack {\frac{{j\left( {{{KL}_{T}L_{R}} + 1} \right)} - n}{\left( {m + 1} \right)_{j}} \cdot \alpha_{n - j}} \right\rbrack}}}$for a positive integer n, (m+1)_(j)=Γ(m+1+j)/Γ(m+1),Γ(z) = ∫₀^(∞)t^(z − 1)𝕖^(−t) 𝕕t for an arbitrary positive number z, andn′ is an arbitrary positive integer.
 5. The evaluation device as claimedin claim 1, each of the receivers having a number L_(R) of receiveantennas under a transmit selective combining/receive selectivecombining (SC/SC) scheme, the transmitter having a number L_(T) oftransmit antennas, wherein when the fading parameter m is greater thanor equal to ½, and the average SNR Q is greater than a predeterminedvalue, said error rate computing module is operable to compute the biterror rate P_(BER) based upon${P_{BER} = \frac{{\Gamma\left( {{{mKL}_{T}L_{R}} + 0.5} \right)} \cdot \left( {m/\overset{\_}{Q}} \right)^{{mKL}_{T}L_{R}}}{2{\sqrt{\pi}\left\lbrack {\Gamma\left( {m + 1} \right)} \right\rbrack}^{{KL}_{T}L_{R}}}},$where Γ(z) = ∫₀^(∞)t^(z − 1)𝕖^(−t) 𝕕t for an arbitrary positive numberz.
 6. The evaluation device as claimed in claim 1, each of the receivershaving a number L_(R) of receive antennas under a transmit selectivecombining/receive selective combining (SC/SC) scheme, the transmitterhaving a number L_(T) of transmit antennas, wherein when the fadingparameter m is a positive integer, said error rate computing module isoperable to compute the bit error rate P_(BEER) based upon${P_{BER} = {\frac{1}{2\sqrt{\pi}}{\sum\limits_{i = 0}^{{KL}_{T}L_{R}}\;{\begin{pmatrix}{{KL}_{T}L_{R}} \\i\end{pmatrix}\left( {- 1} \right)^{i}{\sum\limits_{n = 0}^{i{({m - 1})}}\;\frac{{\beta_{n} \cdot \left( {m/\overset{\_}{Q}} \right)^{n}}{\Gamma\left( {n + 0.5} \right)}}{\left( {1 + {{mi}/\overset{\_}{Q}}} \right)^{n + 0.5}}}}}}},$where Q is the average SNR, β₀=1,$\beta_{n} = {\frac{1}{n}{\sum\limits_{j = 1}^{\min{({n,{m - 1}})}}\left\lbrack {\frac{{j\left( {i + 1} \right)} - n}{j!} \cdot \beta_{n - j}} \right\rbrack}}$for a positive integer n, ${\begin{pmatrix}{{KL}_{T}L_{R}} \\i\end{pmatrix} = \frac{\left( {{KL}_{T}L_{R}} \right)!}{{i!}{\left( {{{KL}_{T}L_{R}} - i} \right)!}}},$and Γ(z) = ∫₀^(∞)t^(z − 1)𝕖^(−t) 𝕕t for an arbitrary positive number z.7. The evaluation device as claimed in claim 1, each of the receivershaving a number L_(R) of receive antennas under a transmit selectivecombining/receive maximum ratio combining (SC/MRC) scheme, thetransmitter having a number L_(T) of transmit antennas, wherein when thefading parameter m is greater than or equal to ½, said error ratecomputing module is operable to compute the bit error rate _(PEER) basedupon${P_{BER} = {\frac{1}{2\sqrt{\pi}}{\sum\limits_{n = 0}^{n^{\prime}}\frac{{\alpha_{n} \cdot \left( {m/\overset{\_}{Q}} \right)^{{{mKL}_{T}L_{R}} + n}}{\Gamma\left( {{{mKL}_{T}L_{R}} + n + 0.5} \right)}}{\left( {1 + {{mKL}_{T}/\overset{\_}{Q}}} \right)^{{{mKL}_{T}L_{R}} + n + 0.5}}}}},$where Q is the average SNR,${\alpha_{0} = \left\lbrack \frac{1}{\Gamma\left( {m + 1} \right)} \right\rbrack^{{KL}_{T}}},$and$\alpha_{n} = {\frac{1}{n}{\sum\limits_{j = 1}^{n}\left\lbrack {\frac{{j\left( {{KL}_{T} + 1} \right)} - n}{\left( {{mL}_{R} + 1} \right)_{j}} \cdot \alpha_{n - j}} \right\rbrack}}$for a positive integer n, (mL_(R)+1)_(j)=Γ(mL_(R)+1+j)/Γ(mL_(R)+1),Γ(z) = ∫₀^(∞)t^(z − 1)𝕖^(−t) 𝕕t for an arbitrary positive number z, andn′ is an arbitrary positive integer.
 8. The evaluation device as claimedin claim 1, each of the receivers having a plurality of receive antennasunder a transmit selective combining/receive maximum ratio combining(SC/MRC) scheme, the transmitter having a number L_(T) of transmitantennas, wherein when the fading parameter m is greater than or equalto ½, and the average SNR Q is greater than a predetermined value, saiderror rate computing module is operable to compute the bit error rateP_(BER) based upon${P_{BER} = \frac{{\Gamma\left( {{{mKL}_{T}/\overset{\_}{Q}} + 0.5} \right)} \cdot \left( {mL}_{R} \right)^{{mKL}_{T}/\overset{\_}{Q}}}{2{\sqrt{\pi}\left\lbrack {\Gamma\left( {{m/\overset{\_}{Q}} + 1} \right)} \right\rbrack}^{{KL}_{T}}}},$where Γ(z) = ∫₀^(∞)t^(z − 1)𝕖^(−t) 𝕕t for an arbitrary positive numberz.
 9. The evaluation device as claimed in claim 1, each of the receivershaving a number L_(R) of receive antennas under a transmit selectivecombining/receive maximum ratio combining (SC/MRC) scheme, thetransmitter having a number L_(T) of transmit antennas, wherein when thefading parameter m is a positive integer, said error rate computingmodule is operable to compute the bit error rate P_(BER) based upon${P_{BER} = {\frac{1}{2\sqrt{\pi}}{\sum\limits_{i = 0}^{{KL}_{T}}{\begin{pmatrix}{KL}_{T} \\i\end{pmatrix}\left( {- 1} \right)^{i}{\sum\limits_{n = 0}^{{\mathbb{i}}{({{mL}_{R} - 1})}}\frac{{\beta_{n} \cdot \left( {m/\overset{\_}{Q}} \right)^{n}}{\Gamma\left( {n + 0.5} \right)}}{\left( {1 + {{mi}/\overset{\_}{Q}}} \right)^{n + 0.5}}}}}}},$where Q is the average SNR, β₀=1,$\beta_{n} = {\frac{1}{n}{\sum\limits_{j = 1}^{\min{({n,{{mL}_{R} - 1}})}}\left\lbrack {\frac{{j\left( {i + 1} \right)} - n}{j!} \cdot \beta_{n - j}} \right\rbrack}}$for a positive integer n, ${\begin{pmatrix}{KL}_{T} \\i\end{pmatrix} = \frac{\left( {KL}_{T} \right)!}{{i!}{\left( {{KL}_{T} - i} \right)!}}},$and Γ(z) = ∫₀^(∞)t^(z − 1)𝕖^(−t) 𝕕t for an arbitrary positive number z.10. The evaluation device as claimed in claim 1, each of the receivershaving a number L_(R) of receive antennas under a space-time block codes(STBC) scheme, the transmitter having a number L_(T) of transmitantennas, wherein when the fading parameter m is greater than or equalto ½, said error rate computing module is operable to compute the biterror rate P_(BER) based upon${P_{BER} = {\frac{1}{2\sqrt{\pi}}{\sum\limits_{n = 0}^{n^{\prime}}\frac{{\alpha_{n} \cdot \left( {{mL}_{T}/\overset{\_}{Q}} \right)^{{{mKL}_{T}L_{R}} + n}}{\Gamma\left( {{{mKL}_{T}L_{R}} + n + 0.5} \right)}}{\left( {1 + {{mKL}_{T}/\overset{\_}{Q}}} \right)^{{{mKL}_{T}L_{R}} + n + 0.5}}}}},$where Q is the average SNR,${\alpha_{0} = \left\lbrack \frac{1}{\Gamma\left( {{{mL}_{T}L_{R}} + 1} \right)} \right\rbrack^{K}},{\alpha_{n} = {\frac{1}{n}{\sum\limits_{j = 1}^{n}\left\lbrack {\frac{{j\left( {K + 1} \right)} - n}{\left( {{{mL}_{T}L_{R}} + 1} \right)_{j}} \cdot \alpha_{n - j}} \right\rbrack}}}$for a positive integer n,(mL_(T)L_(R)+1)_(j)=Γ(mL_(T)L_(R)+1+j)/Γ(mL_(T)L_(R)+1),Γ(z) = ∫₀^(∞)t^(z − 1)𝕖^(−t) 𝕕t for an arbitrary positive number z, andn′ is an arbitrary positive integer.
 11. The evaluation device asclaimed in claim 1, each of the receivers having a plurality of receiveantennas under a space-time block codes (STBC) scheme, the transmitterhaving a number L_(T) of transmit antennas, wherein when the fadingparameter m is greater than or equal to ½, and the average SNR Q isgreater than a predetermined value, said error rate computing module isoperable to compute the bit error rate P_(BER) based upon${P_{BER} = \frac{{\Gamma\left( {{{mKL}_{T}L_{R}} + 0.5} \right)} \cdot \left( {{mL}_{T}/\overset{\_}{Q}} \right)^{{mKL}_{T}L_{R}}}{2{\sqrt{\pi}\left\lbrack {\Gamma\left( {{{mL}_{T}L_{R}} + 1} \right)} \right\rbrack}^{K}}},$where Γ(z) = ∫₀^(∞)t^(z − 1)𝕖^(−t) 𝕕t for an arbitrary positive numberz.
 12. The evaluation device as claimed in claim 1, each of thereceivers having a number L_(R) of receive antennas under a space-timeblock codes (STBC) scheme, the transmitter having a number L_(T) oftransmit antennas, wherein when the fading parameter m is a positiveinteger, said error rate computing module is operable to compute the biterror rate P_(BER) based upon${P_{BER} = {\frac{1}{2\sqrt{\pi}}{\sum\limits_{i = 0}^{K}{\begin{pmatrix}K \\i\end{pmatrix}\left( {- 1} \right)^{i}{\sum\limits_{n = 0}^{i{({{{mL}_{T}L_{R}} - 1})}}\frac{{\beta_{n} \cdot \left( {{mL}_{T}/\overset{\_}{Q}} \right)^{n}}{\Gamma\left( {n + 0.5} \right)}}{\left( {1 + {{miL}_{T}/\overset{\_}{Q}}} \right)^{n + 0.5}}}}}}},$where Q is the average SNR, β₀=1,$\beta_{n} = {\frac{1}{n}{\sum\limits_{j = 1}^{\min{({n,{{{mL}_{T}L_{R}} - 1}})}}\left\lbrack {\frac{{j\left( {i + 1} \right)} - n}{j!} \cdot \beta_{n - j}} \right\rbrack}}$for a positive integer n, ${\begin{pmatrix}K \\i\end{pmatrix} = \frac{(K)!}{{i!}{\left( {K - i} \right)!}}},$ andΓ(z) = ∫₀^(∞)t^(z − 1)𝕖^(−t) 𝕕t for an arbitrary positive number z. 13.The evaluation device as claimed in claim 1, further comprising: athreshold value computing module operable to compute a threshold valuebased upon a given capacity; and an outage probability computing moduleoperable, based upon the fading parameter, the number of the receivers,the average SNR and the threshold value, to compute an outageprobability of the transceiver system corresponding to the givencapacity; said output module being operable to provide the transceiversystem with the average SNR, the bit error rate and the outageprobability as the performance information of the transceiver system.